Problem 5 Evaluate. Assume the variable do... [FREE SOLUTION]

Chapter 2: Problem 5

Evaluate. Assume the variable does not equal zero. $$-2 k^{0}$$

Short Answer

Expert verified

The evaluated expression $-2k^0$ simplifies to $-2$, as any nonzero number raised to the power of zero is equal to one. $-2(1) = -2$.

Step by step solution

Apply the Rule k^0 = 1

Since any nonzero number raised to the power of zero is equal to one, we can replace $k^0$ with 1. \[-2k^0 = -2(1)\]

Simplify the Expression

Now that we've replaced $k^0$ with 1, we can simplify the expression by multiplying $-2$ with $1$. \[-2(1) = -2\] The evaluated expression is $-2$.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions

Simplifying expressions involves finding a simpler form of an expression without changing its value. This is an essential math skill that helps make calculations easier and clearer. When you see a mathematical expression to be simplified, look for common rules or patterns that apply, such as combining like terms or applying exponent rules. For example, in the exercise $-2k^0$, you simplify the expression by first dealing with the exponent, which leads you to $-2(1)$. This step-by-step reduction is what we call simplifying. Breaking down complex expressions in this way ensures that you understand each component and operation performed, leading to the final answer.

Exponents

Exponents tell us how many times we multiply a number by itself. An exponent is represented by a small number written to the top-right of a base number. In the expression $k^0$, $k$ is the base, and $0$ is the exponent.There are a few simple rules that guide how exponents work:

Zero Exponent Rule: Any base raised to the power of zero equals one, $a^0 = 1$ for any number $a$, as long as $a$ is not zero.
Product Rule: To multiply like bases with exponents, you add the exponents, $a^m \times a^n = a^{m+n}$.
Power Rule: For exponents raised to another power, multiply the exponents, $(a^m)^n = a^{m \times n}$.

In the exercise, the application of the zero exponent rule simplifies $k^0$ to $1$, since any number to the power of zero is one, as long as the base is not zero.

Evaluating Expressions

Evaluating expressions is the process of finding the value of the expression when the variables have been defined. This often involves using rules and formulas to calculate and reach a final number. In the provided exercise, you start with $-2k^0$. Thanks to the zero exponent rule, $k^0$ gets replaced by $1$. Then, you multiply the remaining terms, resulting in $-2 \times 1$. This is the evaluation step鈥攖aking the simplified expression and performing the necessary arithmetic to find the value, which in this case is $-2$. It's important to follow each operation carefully, ensuring an accurate result every time.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Evaluate. Assume the variable does not equal zero. $$-2 k^{0}$$

Short Answer

Step by step solution

Apply the Rule k^0 = 1

Simplify the Expression

Key Concepts

Simplifying Expressions

Exponents

Evaluating Expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.